Prohairetic Deontic Logic (PDL)

  • Leendert W. N. van der Torre
  • Yao-Hua Tan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1489)

Abstract

In this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based dyadic deontic logic. An obligation ‘α should be (done) if β is (done)’ is true if (1) no ¬αβ state is as preferable as an αβ state and (2) the preferred β states are α states. We show that the different elements of this mixed representation solve different problems of deontic logic. The first part of the definition is used to formalize contrary-to-duty reasoning, that for example occurs in Chisholm’s and Forrester’s notorious deontic paradoxes. The second part is used to make dilemmas inconsistent. PDL shares the intuitive semantics of preference-based deontic logics without introducing additional semantic machinery such as bi-ordering semantics or ceteris paribus preferences.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C.E. Alchourrón. Philosophical foundations of deontic logic and the logic of defeasible conditionals. In J.-J. Meyer and R. Wieringa, editors, Deontic Logic in Computer Science: Normative System Specification, pages 43–84. John Wiley & Sons, 1993.Google Scholar
  2. 2.
    L. Åqvist. Good Samaritans, contrary-to-duty imperatives, and epistemic obligations. Noûs, 1:361–379, 1967.CrossRefGoogle Scholar
  3. 3.
    C. Boutilier. Conditional logics of normality: a modal approach. Artificial Intelligence, 68:87–154, 1994.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A.L. Brown, S. Mantha, and T. Wakayama. Exploiting the normative aspect of preference: a deontic logic without actions. Annals of Mathematics and Artificial Intelligence, 9:167–203, 1993.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    B.F. Chellas. Modal Logic: An Introduction. Cambridge University Press, 1980.Google Scholar
  6. 6.
    R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33–36, 1963.CrossRefGoogle Scholar
  7. 7.
    R. Conte and R. Falcone. ICMAS’96: Norms, obligations, and conventions. AI Magazine, 18,4:145–147, 1997.Google Scholar
  8. 8.
    B.S. Firozabadhi and L.W.N. van der Torre. Towards an analysis of control systems. In H. Prade, editor, Proceedings of the ECAI’98, pages 317–318, 1998.Google Scholar
  9. 9.
    J.W. Forrester. Gentle murder, or the adverbial Samaritan. Journal of Philosophy, 81:193–197, 1984.CrossRefMathSciNetGoogle Scholar
  10. 10.
    L. Goble. A logic of good, would and should, part 2. Journal of Philosophical Logic, 19:253–276, 1990.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    L. Goble. Murder most gentle: the paradox deepens. Philosophical Studies, 64:217–227, 1991.CrossRefGoogle Scholar
  12. 12.
    B. Hansson. An analysis of some deontic logics. In R. Hilpinen, editor, Deontic Logic: Introductionary and Systematic Readings, pages 121–147. D. Reidel Publishing Company, Dordrecht, Holland, 1971. Reprint from Noûs, 1969.Google Scholar
  13. 13.
    S.O. Hansson. A new semantical approach to the logic of preference. Erkenntnis, 31:1–42, 1989.CrossRefGoogle Scholar
  14. 14.
    S.O. Hansson. Defining “good” and “bad” in terms of “better”. Notre Dame Journal of Formal Logic, 31:136–149, 1990.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    S.O. Hansson. Preference-based deontic logic (PDL). Journal of Philosophical Logic, 19:75–93, 1990.CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    S.O. Hansson. Situationist deontic logic. Journal of Philosophical Logic, 26:423–448, 1997.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Z. Huang and M. Masuch. The logic of permission and obligation in the framework of ALX3: how to avoid the paradoxes of deontic logic. Logique et Analyse, 149, 1997.Google Scholar
  18. 18.
    H.G. Hughes and M.J. Creswell. A Companion to Modal Logic. Methuen, London, 1984.Google Scholar
  19. 19.
    F. Jackson. On the semantics and logic of obligation. Mind, 94:177–196, 1985.CrossRefMathSciNetGoogle Scholar
  20. 20.
    R.E. Jennings. Can there be a natural deontic logic? Synthese, 65:257–274, 1985.CrossRefMathSciNetGoogle Scholar
  21. 21.
    P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the KR’91, pages 357–367, 1991.Google Scholar
  22. 22.
    D. Lewis. Counterfactuals. Blackwell, Oxford, 1973.Google Scholar
  23. 23.
    D. Lewis. Semantic analysis for dyadic deontic logic. In S. Stunland, editor, Logical Theory and Semantical Analysis, pages 1–14. D. Reidel Publishing Company, Dordrecht, Holland, 1974.Google Scholar
  24. 24.
    B. Loewer and M. Belzer. Dyadic deontic detachment. Synthese, 54:295–318, 1983.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    J. Pearl. From conditional oughts to qualitative decision theory. In Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI’93), pages 12–20, 1993.Google Scholar
  26. 26.
    H. Prakken and M.J. Sergot. Contrary-to-duty obligations. Studia Logica, 57:91–115, 1996.MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    H. Prakken and M.J. Sergot. Dyadic deontic logic and contrary-to-duty obligations. In D. Nute, editor, Defeasible Deontic Logic, pages 223–262. Kluwer, 1997.Google Scholar
  28. 28.
    Y. Moses R. Fagin, J.Y. Halpern and M.Y. Vardi. Reasoning About Knowledge. MIT press, 1995.Google Scholar
  29. 29.
    S.-W. Tan and J. Pearl. Specification and evaluation of preferences under uncertainty. In Proceedings of the KR’94, pages 530–539, 1994.Google Scholar
  30. 30.
    Y.-H. Tan and L.W.N. van der Torre. How to combine ordering and minimizing in a deontic logic based on preferences. In Deontic Logic, Agency and Normative Systems. Proceedings of the ΔEON’96, Workshops in Computing, pages 216–232. Springer Verlag, 1996.Google Scholar
  31. 31.
    L.W.N. van der Torre. Violated obligations in a defeasible deontic logic. In Proceedings of the ECAI’94, pages 371–375, 1994.Google Scholar
  32. 32.
    L.W.N. van der Torre. Reasoning About Obligations: Defeasibility in Preference-based Deontic Logics. PhD thesis, Erasmus University Rotterdam, 1997.Google Scholar
  33. 33.
    L.W.N. van der Torre and Y.-H. Tan. Cancelling and overshadowing: two types of defeasibility in defeasible deontic logic. In Proceedings of the IJCAI’95, pages 1525–1532, 1995.Google Scholar
  34. 34.
    L.W.N. van der Torre and Y.-H. Tan. Contextual deontic logic. In Proceedings of the First International Conference on Modeling and Using Context (CONTEXT’ 97), pages 1–12, Rio de Janeiro, Brazil, 1997.Google Scholar
  35. 35.
    L.W.N. van der Torre and Y.-H. Tan. The many faces of defeasibility in defeasible deontic logic. In D. Nute, editor, Defeasible Deontic Logic, pages 79–121. Kluwer, 1997.Google Scholar
  36. 36.
    L.W.N. van der Torre and Y.-H. Tan. Diagnosis and decision making in normative reasoning. Artificial Intelligence and Law, 1998.Google Scholar
  37. 37.
    L.W.N. van der Torre and Y.-H. Tan. The temporal analysis of Chisholm’s paradox. In Proceedings of the AAAI’98, 1998.Google Scholar
  38. 38.
    L.W.N. van der Torre and Y.-H. Tan. An update semantics for deontic reasoning. In P. McNamara and H. Prakken, editors, Norms, Logics and Information Systems. New Studies on Deontic Logic and Computer Science. IOS Press, 1998.Google Scholar
  39. 39.
    L.W.N. van der Torre and Y.-H. Tan. An update semantics for prima facie obligations. In H. Prade, editor, Proceedings of the ECAI’98, pages 38–42, 1998.Google Scholar
  40. 40.
    B.C. van Fraassen. Values and the heart command. Journal of Philosophy, 70:5–19, 1973.CrossRefGoogle Scholar
  41. 41.
    G.H. von Wright. The Logic of Preference. Edinburgh University Press, 1963.Google Scholar
  42. 42.
    G.H. von Wright. A new system of deontic logic. In R. Hilpinen, editor, Deontic Logic: Introductory and Systematic Readings, pages 105–120. D. Reidel Publishing company, Dordrecht, Holland, 1971.Google Scholar
  43. 43.
    E. Weydert. Hyperrational conditionals. monotonic reasoning about nested default conditionals. In Foundations of Knowledge Representation and Reasoning, LNAI 810, pages 310–332. Springer, 1994.Google Scholar
  44. 44.
    R.J. Wieringa and J.-J.Ch. Meyer. Applications of deontic logic in computer science: A concise overview. In Deontic Logic in Computer Science, pages 17–40. John Wiley & Sons, Chichester, England, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Leendert W. N. van der Torre
    • 1
  • Yao-Hua Tan
    • 2
  1. 1.IRITPaul Sabatier UniversityToulouseFrance
  2. 2.EuridisErasmus University RotterdamThe Netherlands

Personalised recommendations